Work

A new method for constructing multi-component integrable hierarchies with KdV case

Year: 2026

Type: article

Abstract: In the field of nonlinear integrable systems, the investigation of the multi-component extensions of these systems is of great significance. In this paper, we present a novel method for constructing multi-component integrable hierarchies, with the Korteweg–de Vries (KdV) case used as an illustration. Based on a specific spectral problem, we propose a three-component generalized KdV hierarchy by applying the zero-curvature equation. Note that in the first system of this hierarchy, one of the equations is u t = 1 32 ( p + q + 2 u ) x x x − 3 16 ( p + q + 2 u ) ( p x + q x + 2 u x ) + w 21 , x , where w 21 = w 21 ( p , q , u , p x , q x , u x , ⋯ ) is an arbitrary function. Upon choosing a specific function, this system reduces to the KdV equation.

Source: Communications in Theoretical Physics

DOI: 10.1088/1572-9494/ae6e30

Authors: Hong-Qian Sun, Shou-Feng Shen, Wen-Xiu Ma

Institutions: Zhejiang University of Technology, Zhejiang Normal University, King Abdulaziz University, University of South Florida, North-West University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: bronze

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation

Awards: G1182344820, G2000674461, G3871874060